On the exact quantum scale invariance of three-dimensional reduced QED theories

Abstract

An effective quantum field theory description of graphene in the ultra-relativistic regime is given by reduced QED aka. pseudo QED aka. mixed-dimensional QED. It has been speculated in the literature that reduced QED constitutes an example of a specific class of hard-to-find theories: an interacting CFT in more than two dimensions. This speculation was based on two-loop perturbation theory. Here, we give a proof of this feature, namely the exact vanishing of the b-function, thereby showing that reduced QED can effectively be considered as an interacting (boundary) CFT, underpinning recent work in this area. The argument, valid for both two- and four-component spinors, also naturally extends to an exactly marginal deformation of reduced QED, thence resulting in a non-supersymmetric conformal manifold. The latter corresponds to boundary layer fermions between two different dielectric half-spaces.

arXiv commentv2: improved discussion about boundary conditions and added references

References in corpus (37)

• The electronic properties of graphene
• Topological Field Theory of Time-Reversal Invariant Insulators
• Gauge fields in graphene
• Dirac cones reshaped by interaction effects in suspended graphene
• Non-Fermi liquid behaviour of electrons in the half-filled honeycomb lattice (A renormalization group approach)
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Is the Composite Fermion a Dirac Particle?
• Tuning the effective fine structure constant in graphene: opposing effects of dielectric screening on short- and long-range potential scattering
• Particle-Vortex Duality from 3d Bosonization
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Chiral Gauge Theory for Graphene
• Boundary Conformal Field Theory and a Boundary Central Charge
• Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory
• Dynamical Chiral Symmetry Breaking on a Brane in Reduced QED
• Electromagnetic current correlations in reduced quantum electrodynamics
• Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response
• Scale-invariance of parity-invariant three-dimensional QED
• On bosonization in $3$ dimensions
• Interaction Induced Quantum Valley Hall Effect in Graphene
• Edge Dynamics from the Path Integral: Maxwell and Yang-Mills
• Decoding a Three-Dimensional Conformal Manifold
• Bosonisation in Three-Dimensional Quantum Field Theory
• A comment on bosonization in $d\ge 2$ dimensions
• Scale invariance implies conformal invariance for the three-dimensional Ising model
• O(1/N_f) Corrections to the Thirring Model in 2<d<4
• On non-supersymmetric conformal manifolds: field theory and holography
• Renormalization group aspects of graphene
• Chiral-Symmetry Breaking in Pseudo Quantum Electrodynamics at Finite Temperature
• Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids
• Topological and Universal Aspects of Bosonized Interacting Fermionic Systems in (2+1)d
• Comments on the Chern-Simons photon term in the QED description of graphene
• Conformal Manifolds with Boundaries or Defects
• The ultraviolet and infrared perturbative finiteness of massless QED${}_3$
• On general ultraviolet properties of a class of confining propagators
• Conformal QED in two-dimensional topological insulators
• Exact critical exponents for vector operators in the 3d Ising model and conformal invariance

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• 3d Abelian Gauge Theories at the Boundary
• Conformal Surface Defects in Maxwell Theory are Trivial
• Torsion in quantum field theory through time-loops on Dirac materials
• Renormalization and conformal invariance of non-local quantum electrodynamics
• The Casimir energy in terms of boundary quantum field theory: the QED case
• Torsion at different scales: from materials to the Universe
• Electron-Photon Vertex and Dynamical Chiral Symmetry Breaking in Reduced QED: An Advanced Study of Gauge Invariance
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Half-integer anomalous currents in 2D materials from a QFT viewpoint
• Polyakov's confinement mechanism for generalized Maxwell theory
• Aspects of the pseudo Chiral Magnetic Effect in 2D Weyl-Dirac Matter
• Effects of the two-dimensional Coulomb interaction in both Fermi velocity and energy gap for Dirac-like electrons at finite temperature
• Reduced quantum electrodynamics in curved space
• The quantum scale invariance in graphene-like quantum electrodynamics
• Non-perturbative field theoretical aspects of graphene and related systems
• Strongly interacting matter in extreme magnetic fields
• Quantization of a Self-dual Conformal Theory in (2+1) Dimensions
• Defect QED: Dielectric without a Dielectric, Monopole without a Monopole
• Reduced QED with few planes and fermion gap generation
• Thermoelectric properties and Wiedemann-Franz like relations in mixed-dimensional QEDs from particle-vortex dualities
• Critical properties of three-dimensional many-flavour QEDs
• Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation
• On the ultraviolet finiteness of parity-preserving $U(1)\times U(1)$ massive QED${}_3$
• Time-loops to spot torsion on bidimensional Dirac materials with dislocations
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene